A computation of the covariance between two linear statistics for the Jellium model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915358933254144 |
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| author | Rigas, Pete |
| author_facet | Rigas, Pete |
| contents | We extend previous results providing an exact formula for the variance of a linear statistic for the Jellium model, a one-dimensional model of Statistical mechanics obtained from the $k \longrightarrow 0^{+}$ limit of the Dyson log-gas. For such a computation of the covariance, in comparison to previous work for computations of the log-gas covariance, we obtain a formula between two linear statistics, given arbitrary functions $f$ and $g$ over the real line, that is dependent upon an asymptotic approximation of the Jellium probability distribution function from large $N$ deviations, and from an effective saddle-point action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01948 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A computation of the covariance between two linear statistics for the Jellium model Rigas, Pete Statistical Mechanics Probability We extend previous results providing an exact formula for the variance of a linear statistic for the Jellium model, a one-dimensional model of Statistical mechanics obtained from the $k \longrightarrow 0^{+}$ limit of the Dyson log-gas. For such a computation of the covariance, in comparison to previous work for computations of the log-gas covariance, we obtain a formula between two linear statistics, given arbitrary functions $f$ and $g$ over the real line, that is dependent upon an asymptotic approximation of the Jellium probability distribution function from large $N$ deviations, and from an effective saddle-point action. |
| title | A computation of the covariance between two linear statistics for the Jellium model |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2212.01948 |